Simplify the following expression: $\dfrac{21t^3}{14t}$ You can assume $t \neq 0$.
Explanation: $ \dfrac{21t^3}{14t} = \dfrac{21}{14} \cdot \dfrac{t^3}{t} $ To simplify $\frac{21}{14}$ , find the greatest common factor (GCD) of $21$ and $14$ $21 = 3 \cdot 7$ $14 = 2 \cdot 7$ $ \mbox{GCD}(21, 14) = 7 $ $ \dfrac{21}{14} \cdot \dfrac{t^3}{t} = \dfrac{7 \cdot 3}{7 \cdot 2} \cdot \dfrac{t^3}{t} $ $\phantom{ \dfrac{21}{14} \cdot \dfrac{3}{1}} = \dfrac{3}{2} \cdot \dfrac{t^3}{t} $ $ \dfrac{t^3}{t} = \dfrac{t \cdot t \cdot t}{t} = t^2 $ $ \dfrac{3}{2} \cdot t^2 = \dfrac{3t^2}{2} $